|Dear Olivier, dear Femke,|
Dear Sangeetika, Svetlana and Jana,
I have read the response to both Femke and I and I had a peek at the tracked change revised paper. I believe that the authors did a remarkable job in their revision and answers to the reviewers. My opinion is that the paper is now acceptable.
That said, beyond the two minor remarks listed below, there is one important third suggestion that I believe need to be addressed.
- In the beginning of section 2, "we will also proposed" -> "we will also propose".
- The usage is to systematically use an article "the" (possibly "an") before EnKF and ETKF, and any variant thereof. Please correct this throughout the manuscript.
- Very important: The EKI that you use (or any variant thereof) is NOT at all an EnKF, neither from a mathematical nor from an applied standpoint. The EKI you implement is an "Iterative ensemble smoother". This is a mathematically consistent definition as well as the one accepted in the oil reservoir community as of today. (Substantially) Generalised to the (time) sequential framework of meteorology and oceanography, this is called the Iterative ensemble Kalman smoother (Bocquet and Sakov, "An iterative ensemble Kalman smoother", QJRMS, 2014).
Why cannot it be called the EnKF?
First, the EnKF has a very precise definition and is very widely used (Evensen, Springer, 2009), which is quite far from the EKI and similar methods.
Second, when Geir Evensen came to the oil reservoir R&D community, he applied the (stochastic) EnKF in an iterative fashion over a time window (but not sequentially in time as meteorology and oceanography) for state and parameter estimation. He was followed by many researchers in the field. Then, he/they realised that it was mathematically incorrect and that what he was actually after is the (iterative) ensemble smoother (which comes with a relaxation term to the prior compared to a naive iterative application of the EnKF throughout the time window). "Kalman" is dropped to avoid getting confused with the sequential in time variant of the scheme, and because, as a nonlinear iterative scheme, the Gaussian assumption is dropped, except for the priors. The fun comes from the fact that he was the one (with Peter Jan van Leeuwen) to introduce the classical (not iterative) EnKS in the geophysical community and might have realised this earlier (Evensen and van Leeuwen, MWR, 2000). Note that Steve Cohn et al had introduced the Kalman smoother much earlier in the geophysical community (Cohn et al, MWR, 1994).
"Iterative ensemble smoother" is primarily a mathematical definition -- the term smoother is very well defined (see the book by Anderson and Moore, "Optimal filtering", Prentice-Hall, Inc, 1979). Even though "Iterative ensemble smoother" is the term ultimately used by Geir for his own implementation, it is semantically quite generic and covers several variants. The EKI is an (mathematically correct!) iterative ensemble smoother.
If I am not clear enough, please do not hesitate to contact me. There is also the possibility that my understanding is not accurate enough.